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					              Planetary gearing
        Planetary gearing

  i     Calculation without errors.                                                       Sun                 Planet             Ring gear
 ii        Project information
 ?                                                                   Input section
 1.0       Options of basic input parameters
 1.1 Calculation units                                                             SI Units (N, mm, kW…)

 1.2 Transmission type (input/output)                                              Sun               => Planet Carrier

 1.3 Transferred power                                                  Pw [kW]           19.51                -19.51               0.00
 1.4 Speed (Sun, Planet Carrier, Ring Gear)                                   n          3000.00              548.39                0.00             [/min]
 1.5 Requested speed for the: Planet Carrier                                  n          400.00                   253.73 ~ 750
 1.6 Torsional moment (Sun, Planet Carrier, Ring Gear)                       Mk           62.11               -339.79             277.68             [Nm]
 1.7 Speed (Planet in Planet Carrier)                                         n                               -1389.25                               [/min]
 1.8 Transmission ratio z1/z0, z2/z1, (z2/z0)                                  i          1.765                -2.533             (-4.471)
 2.0       Options of material, loading conditions, operational and production parameters
 2.1 Material identification according standard :                                            DIN

 2.2 Material of the sun :                                                         C...Alloy structural steel 37 Cr 4 (Rm=883 MPa) heat treated

 2.3 Material of the planet :                                                      C...Alloy structural steel 37 Cr 4 (Rm=883 MPa) heat treated

 2.4 Material of the ring gear :                                                   C...Alloy structural steel 37 Cr 4 (Rm=883 MPa) heat treated

 2.5 Loading of the gearbox, driving machine - examples                                      A...Continuous

 2.6 Loading of gearbox, driven machine - examples                                           A...Continuous

 2.7 Type of gearing mounting                                                                Double-sided symmetrically supported gearing - type 1

 2.8 Accuracy grade - ISO1328 |Ra max|v max                                                  6…....(Ra max.= 1.6 / v max.= 30)

 2.9 Desired service life                                                    Lh                                20000                       [h]
2.10 Coefficient of safety (contact/bend)                               SH / SF                     1.30                 1.60
2.11 Automatic design
 3.0       Parameters of the cutting tool and tooth profile
 3.1 Standardized tool                               2. DIN 867 (a=20deg, ha0=1.25, hf0=1.0, ra0=0.25, d0=0deg, anp=0deg, ca=0.25)

 3.2 Addendum of tool                                                     ha0*           1.2500               1.2500              1.2500             [modul]
 3.3 Dedendum of tool                                                      hf0*          1.0000               1.0000              1.2000             [modul]
 3.4 Fillet radius of tool                                                 ra0*          0.2500               0.2500              0.0000             [modul]
 3.5 Root fillet radius of tool                                            rf0*          0.0000               0.0000              0.3800             [modul]
 3.6 Chamfer of root                                                       cha*          0.0000               0.0000              0.0000             [modul]
 3.7 Chamfer of root                                                       chb*          0.0000               0.0000              0.0000             [modul]
 3.8 Protuberance hight                                                     δ0*          0.0000               0.0000              0.0000             [modul]
 3.9 Protuberance angle                                                    αnp           0.0000               0.0000              0.0000             [°]
3.10 Min. unit head clearance                                            ca*min          0.2500               0.2500              0.1000             [modul]
3.11 Unit head clearance                                                    ca*          0.2500               0.3047                                 [modul]
3.12 Unit head clearance                                                    ca*                               0.3047              0.2500             [modul]
3.13 Number of Teeth of the cutting tool                                     z0                                                      30
3.14 Addendum modification coefficient                                      x0*                                                     0.00             [modul]
3.15 Tip diameter of the tool                                               da0                                                   103.276            [mm]

Sun                               5.00

                                  4.00

                                  3.00

                                  2.00

                                  1.00

                                  0.00
-6.00       -4.00     -2.00          0.00   2.00     4.00        6.00
                                -1.00

                                -2.00

                                -3.00

                                -4.00

                                -5.00


 4.0       Design of a module and geometry of toothing




 4.1 Number of Planets                                                                                           3            <= 4     3
 4.2 Number of teeth - setting                                                                      Optimal (30)

 4.3 Number of teeth (Sun, Planet, Ring Gear)                                z          17                   30                   -76
 4.4 Speed (Sun, Planet Carrier, Ring Gear)                                 n      3000.00                548.39                  0.00        [/min]
 4.5 Normal pressure angle                                                  α                                20                               [°]
 4.6 Helix angle                                                            β                                20                               [°]
 4.7 Setting of the ratio of the width of the sun to its diameter
 4.8 The ratio of the sun width to its diameter                       ψd / max                    1.00                < 1.4
 4.9 Module / Standardized value                                           mn                      3                                          [mm]
4.10 Diametral Pitch (Citrcular Pitch)                                      P                   32.0000
4.11 Reference diameter                                              d0/d1/d2      54.273                  95.776               -242.633      [mm]
4.12 Recommended width of gearing                                                                         30.4 - 76                           [mm]
4.13 Face width (Sun, Planet, Ring Gear)                             b0/b1/b2      54.000                  56.000                55.000       [mm]
4.14 Working face width                                                    bw                    54.000               55.000                  [mm]
4.15 The ratio of the gear width to its diameter                           ψd          0.99                 0.58                  0.23
4.16 Working center distance                                               aw                    75.025               -75.025                 [mm]
4.17 Approximate weight of the gearing                                      m          0.956               9.345                 3.574        [kg]
4.18 Minimum coefficient of safety                                     SH / SF                    1.42                10.24
4.19 Movement of gears (step and current angle)                                         10                   0             [°]                [°]

                                         150




                                         100




                                          50




                                           0
  -150          -100          -50               0        50          100         150




                                          -50




                                         -100




                                         -150


4.20 Normal backlash
4.21 - Recommended min. | max. value                                                             0.0520               0.2079                  [mm]
4.22 - Selected normal backlash                                             jn                   0.0000               0.0000                  [mm]
5.0      Correction of toothing (Addendum modification)
 5.1 Types
 5.2 - Permissible undercutting of teeth (min. value)                                  -0.235              -0.567                             [modul]
 5.3 - Preventing undercutting of teeth (min. value)                                   -0.118              -0.500                             [modul]
 5.4 - Prevents tapering of teeth (min. value)                                         0.219               -0.731                             [modul]
 5.5 Planet addendum modification coefficient setting                                                                                          x1min
 5.6 Addendum modification coefficient (Sun, Planet, Ring Gear)       x0,x1,x2     0.0000                  0.0000               -0.5682       >-2.2619
 5.7 Sum of addendum modification coefficients - limit              Σx [modul]                  >-1.1488            <1.1244
 5.8 Sum of addendum modification coefficients (x0+x1, x1+x2)       Σx [modul]                   0.0000               -0.5682
 5.9 Center distance (working)                                       aw [mm]                    75.0245             -75.0246
5.10 Required axis distance                                          aw [mm]      150.0491                 72.02 ~ 78.02
5.11 Transverse contact ratio                                              εα                    1.4251               1.5993
5.12 Total contact ratio                                                   εγ                    3.3847               3.5952
5.13 Unit tooth thickness on the tip diameter                             sa*      0.7537                  0.8646                0.8733       [modul]
5.14 Specific sliding on tooth root                                  ϑA0/ϑE1       -3.4858                -1.6917
5.15 Specific sliding on tooth tip                                   ϑE0/ϑA1       0.6285                  0.7771
5.16 Specific sliding on tooth root                                  ϑA1/ϑE2                              -0.7247               -0.1137
5.17 Specific sliding on tooth tip                                   ϑE1/ϑA2                               0.1021                0.4202
5.18 Sum of all specific slidings                                     Sum|ϑ|                     6.5830               1.3608         Sum = 7.9439
5.19 Safety coefficient for surface durability                             SH          1.42                 1.42                  3.15
5.20 Safety coefficient for bending durability                             SF          14.90               10.24                 15.05
5.21 Display of tooth and tool turn for:                         Sun                                                               0   [°]

           15.0                                                                                                 6.0
                                                                                                                4.0
                                                                                                                2.0
                                                                                                                0.0
           10.0                                                                                                -2.0
                                                                                                               -4.0
                                                                                                               -6.0
                                                                                                               -8.0
            5.0
                                                                                                             -10.0
                                                                                                             -12.0

                                                                                                             12.0
            0.0                                                                                              10.0
-5.0              0.0          5.0           10.0         15.0         20.0                                   8.0
                                                                                                              6.0
                                                                                                              4.0
           -5.0                                                                                               2.0
                                                                                                              0.0
                                                                                                             -2.0
                                                                                                             -4.0
          -10.0                                                                                              -6.0


                                                                 Results section
 6.0     Basic dimensions of gearing




 6.1 Number of teeth (Sun, Planet, Ring Gear)                             z         17                  30                  -76
 6.2 Face width (Sun, Planet, Ring Gear)                                  b    54.0000                56.0000             55.0000      [mm]
 6.3 Normal module                                                     mn                   3.0000              3.0000                 [mm]
 6.4 Transverse module                                                  mt                  3.1925              3.1925                 [mm]
 6.5 Circular pitch                                                       p                 9.4248              9.4248                 [mm]
 6.6 Transverse circular pitch                                           pt                 10.0296             10.0296                [mm]
 6.7 Base circular pitch                                               ptb                  9.3526              9.3526                 [mm]
 6.8 Center distance (pitch)                                              a                 75.0245            -73.4283                [mm]
 6.9 Center distance (production)                                       av                  75.0245            -75.1329                [mm]
6.10 Center distance (working)                                          aw                  75.0245            -75.0246                [mm]
6.11 Pressure angle                                                     α                   20.0000             20.0000                [°]
6.12 Transverse pressure angle                                          αt                  21.1728             21.1728                [°]
6.13 Pressure angle at the pitch cylinder                              αwn                  20.0000             23.2660                [°]
6.14 Transverse pressure angle at the pitch cylinder                   αwt                  21.1729             24.1252                [°]
6.15 Helix angle                                                          β                 20.0000             20.0000                [°]
6.16 Base helix angle                                                  βb                   18.7472             18.7472                [°]
6.17 Tip diameter                                                       da     60.2731               101.4476         -239.8251        [mm]
6.18 Reference diameter                                                  d     54.2731                95.7760         -242.6325        [mm]
6.19 Base diameter                                                      db     50.6094                89.3107         -226.2537        [mm]
6.20 Root diameter                                                       df    46.7731                88.2760         -253.3251        [mm]
6.21 Operating pitch diameter                                           dw     54.2731                95.7760                          [mm]
6.22 Operating pitch diameter                                           dw                            97.8581         -247.9072        [mm]
6.23 Addendum                                                           ha         3.0000             2.8358              1.4037       [mm]
6.24 Dedendum                                                            hf        3.7500             3.7500              5.4546       [mm]
6.25 Tooth thickness on the tip diameter                               sna         2.0963             2.4201              2.4652       [mm]
6.26 Tooth thickness on the tip diameter (transverse)                   sta        2.2611             2.5937              2.6198       [mm]
6.27 Tooth thickness on the pitch diameter                              sn         4.7124             4.7124              3.4715       [mm]
6.28 Tooth thickness on the pitch diameter (transverse)                  st        5.0148             5.0148              3.6943       [mm]
6.29 Tooth thickness on the root diameter                               sb         5.1541             6.1929              8.7423       [mm]
6.30 Unit tooth thickness on the tip diameter                          sa*         0.7537             0.8646              0.8733       [modul]
6.31 Unit head clearance                                               ca*         0.2500       0.305 / 0.305             0.2500       [modul]
6.32 Hlavová vůle                                                       ca         0.7500       0.914 / 0.914             0.7500       [mm]
6.33 Unit correction                                                    ∆Y                  0.0000              -0.0361                [modul]
6.34 Sum of addendum modification coefficients                   Σx01/Σx12                  0.0000              -0.5682                [modul]
6.35 Addendum modification coefficient                                    x        0.0000             0.0000              -0.5682      [modul]
 7.0     Supplemental parameters of gearing
 7.1 Number of teeth                                       z       17                  30                 -76
 7.2 Virtual number of teeth of a helical gear            zn     20.175              35.603             -90.194
       Minimum number of teeth:
 7.3      - Permissible undercutting                   zmin1       13                  13                  15
 7.4      - Without undercutting                       zmin2       15                  15                  18
 7.5      - Without tapering                           zmin3       20                  20                  23
 8.0      Qualitative indices of gearing
 8.1 Transverse contact ratio                             εα               1.4251              1.5993
 8.2 Transverse overlap ratio                             εβ               1.9596              1.9959
 8.3 Total contact ratio                                  εγ               3.3847              3.5952
 8.4 Coefficient of gear unloading                     Cdi/df     0.00                0.70                1.00
 8.5 Resonance speed                                      nE    32404.15            11710.70                           [ /min]
 8.6 Resonance speed                                                                6948.05             2742.65
 8.7 Resonance ratio                                       N               0.0757              0.1999
 8.8 Approximate weight of the gearing                     m      0.96                3.11                3.57         [kg]
 8.9 Losses in the gearing                                 ζ               1.43%               0.77%
8.10 Losses (gearing, bearings, total)                     ζ     0.351               0.047               0.398         [kW]
8.11 Recomended lubricant viscosity                      v50                81                  81                     [mm2/sec]
 9.0      Coefficients for safety calculation
       Common for the gearing
 9.1 Stiffness of a tooth pair                             c'              7.412               8.611
 9.2 Meshing stiffness per unit face width                cγ               9.775               12.480
 9.4 Application factor                                   KA                         1.000
 9.5 Dynamic factor                                       KV               1.146               1.275
 9.6 Number of cycles                                     NK    8.83E+09            1.67E+09            1.97E+09
     For pitting safety calculation
 9.7 Face load factor (contact stress)                   KHβ               1.097               1.077
 9.8 Transverse load factor (contact stress)             KHα               1.589               1.783
 9.9 Total factor of additional loads                     KH               1.998               2.449
9.10 Elasticity factor                                    ZE               189.81              189.81
9.11 Zone factor                                          ZH               2.371               2.205
9.12 Helix angle factor                                Zbeta               0.969               0.969
9.13 Contact ratio factor                               Zeps               0.838               0.791
9.14 Work hardening factor                               ZW                1.000               1.000
9.15 Lubricant factor                                     ZL     0.972               0.972               0.972     Mineral oil

9.16 Peripheral speed factor                              ZV     0.979               0.979               0.979
9.17 Roughness factor affecting surface durability        ZR     0.840               0.840               0.840     Automatic

9.18 Life factor for contact stress                       ZN     0.850               0.850               0.850     n=∞; ZN=0.85

9.19 Single pair tooth contact factor                     ZB               1.000               1.000
       Single pair tooth contact factor                   ZD               1.000               1.000
     For bending safety calculation
9.20 Face load factor (root stress)                      KFβ               1.086               1.068
9.21 Transverse load factor (root stress)                K Fα              1.589               1.783
9.22 Total factor of additional loads                     KF               1.978               2.429
9.23 Helix angle factor                                Ybeta               0.833               0.833
9.24 Contact ratio factor                               Yeps               0.722               0.671
9.25 Notch sensitivity factor                          Ydelta    0.990               0.996               1.072
9.26 Size factor                                          YX     1.000               1.000               1.000
9.27 Tooth-root surface factor                            YR     0.931               0.931               0.931
9.28 Alternating load factor                              YA     1.000               0.700               1.000
9.29 Production technology factor                         YT     1.000               1.000               1.000
9.30 Life factor                                          YN     0.850               0.850               0.850     n=∞; YN=0.85

9.31 Stress correction factor                            YST                         1.000
9.32 Form factor (bending)                               YFa     3.072               2.647               1.489
9.33 Stress correction factor                            YSa     1.563               1.689               3.087
9.34 Tip factor, equal (Yfa x YSa)                       YFS     4.802               4.472               4.597
10.0      Stress and safety coefficients
10.1 Safety coefficient for surface durability       SH (S-P)    1.42                1.42
10.2 Safety coefficient for surface durability       SH (P-R)                        3.15                 3.15
10.3 Safety coefficient for bending durability       SF (S-P)    14.90               11.68
10.4 Safety coefficient for bending durability       SF (P-R)                        10.24               15.05
10.5 Nominal contact stress                          SigmaH0               233.42              95.00                   [MPa]
10.6 Contact stress                                   SigmaH     329.96              329.96                            [MPa]
10.7 Contact stress                                                                  148.67              148.67        [MPa]
10.8 Pitting stress limit                            SigmaHG     468.71              468.71                             [MPa]
 10.9 Pitting stress limit                                                                         468.71               468.71        [MPa]
10.10 Permissible contact stress                                SigmaHP       360.55               360.55                             [MPa]
10.11 Permissible contact stress                                                                   360.55               360.55        [MPa]
10.12 Nominal tooth-root stress                                 SigmaF0       13.61                12.22                              [MPa]
10.13 Nominal tooth-root stress                                                                    11.35                 11.88        [MPa]
10.14 Tooth-root stress                                          SigmaF       26.91                24.17                              [MPa]
10.15 Tooth-root stress                                                                            27.57                 28.85        [MPa]
10.16 Tooth-root stress limit                                   SigmaFG       400.89               282.30                             [MPa]
10.17 Tooth-root stress limit                                                                      282.30               434.15        [MPa]
10.18 Permissible bending stress                                SigmaFP       250.56               176.44                             [MPa]
10.19 Permissible bending stress                                                                   176.44               271.35        [MPa]
11.0       Check dimensions of gearing
 11.1 Number of measured teeth                                        zw           3                  5                     9
 11.2 Number of measured teeth                                        zw           3                  5                     9
 11.3 Chordal dimension                                                W     22.9937              41.3586               80.2576       [mm]
 11.4 Pin/Ball diameter                                                dt     5.2500               5.2500               5.2500        [mm]
 11.5 Pin/Ball diameter                                                dt     5.2500               5.2500               5.2500        [mm]
 11.6 Dimension over pins/balls                                        M     61.4317              103.2660             238.3757       [mm]
12.0       Force conditions (forces acting on the toothing)




 12.1 Tangential force                                                 Ft                762.96               762.96                  [N]
 12.2 Normal force                                                    Fn                 864.03               864.03                  [N]
 12.3 Axial force                                                     Fa      833.08                0.00                -833.08       [N]
 12.4 Radial force                                                     Fr                295.52               -295.52                 [N]
 12.5 Force planet carrier -> planet                                Fc-p                          1509.69                             [N]
 12.6 Centrifugal force on the planet                                 Fc                           338.91                             [N]
 12.7 Radial force on the bearing in planet                           Fb                          1547.26                             [N]
 12.8 Rated torque                                                    Mk      20.70                36.15                 92.56        [Nm]
 12.9 Rated rotational speed                                           n      2451.6              -1389.2               548.4         [/min]
12.10 Bending moment (planet gear)                                    Mo          0.00             28.17                   0.00       [Nm]
12.11 Peripheral speed on the pitch diameter                    v | vmax                 6.967                 < 30                   [m/s]
12.12 Specific load                                                   wt                 14.129                13.87                  [N/mm]
12.13 Unit load                                                      wt*                  4.71                 4.62                   [MPa]
13.0       Parameters of the chosen material
 13.1 Density                                                         Ro     7870.00              7870.00               7870.00       [kg/m^3]
 13.2 Young's Modulus (Modulus of Elasticity)                          E      206.00               206.00               206.00        [GPa]
 13.3 Tensile Strength, Ultimate                                     Rm       883.00               883.00               883.00        [MPa]
 13.4 Tensile Strength, Yield                                      Rp0.2      637.00               637.00               637.00        [MPa]
 13.5 Poison's Ratio                                                              0.30              0.30                   0.30
 13.6 Contact Fatigue Limit                                        SHlim      690.00               690.00               690.00        [MPa]
 13.7 Bending Fatigue Limit                                        SFlim      512.00               512.00               512.00        [MPa]
 13.8 Tooth Hardness - Side                                         VHV           285               285                    285        [HV]
 13.9 Tooth Hardness - Core                                          JHV          285               285                    285        [HV]
13.10 Base Number of Load Cycles in Contact                        NHlim    5.00E+07              5.00E+07             5.00E+07
13.11 Wohler Curve Exponent for Contact                               qH          10                  10                   10
13.12 Base Number of Load Cycles in Bend                           NFlim    3.00E+06              3.00E+06             3.00E+06
13.13 Wohler Curve Exponent for Bend                                  qF           6                  6                     6
                                                              Additions section
14.0       Design of the exact transmission ratio
14.1 Number of teeth (Sun, Planet, Ring Gear)                           z         17                  30                   -76
14.2 Speed (Sun, Planet Carrier, Ring Gear)                      n [/min]    3000.00              548.39                   0.00
14.3 Number of teeth from:                                             z          15                  15
14.4 Number of teeth to:                                               z          50                  50
14.5 Requested speed for the: Planet Carrier                     n [/min]     400.00        700.000        z0=22   z1=35     z2=-92

14.6 Run calculation, transmitting values
15.0       Preliminary design of shaft diameters (steel)
        Recommended shaft diameter for:
 16.1      - Main power-transmitting shafts                           DA      48.46                85.33                 79.78        [mm]
 16.2      - Small, short shafts                                             DB         37.66    66.31           62.00     [mm]
16.0       Approximate module calculation from the existing gear
 16.1 Number of teeth                                                         z          24        35              96
 16.2 Tip diameter                                                           da         131.85   187.70          94.70     [mm]
 16.3 Distance between teeth edges                                            u          0.00     0.00           14.13     [mm]
 16.4 Helix angle                                                             β         10.00    10.00           10.00     [°]
 16.5 Module of tooth                                                        mn         5.0000   5.0000          0.9973    [mm]
17.0       Graphical output, CAD systems
 17.1 2D drawing output to:             DXF File

 17.2 2D Drawing scale                  Automatic

 17.3 Detail:                           Planet

                                                                                                        β [°]…     30
 17.4 Detailed drawing of tooth and wheel                                                        a [modul]…        1
 17.5 Number of drawn teeth                                             4
 17.6 Number of points of tooth tip                                     5
 17.7 Number of points of tooth flank                                   30
 17.8 Rolling (turning) of a tool between the bite                    0.5         [°]               Drawing without axes
 17.9 Number of tooth copies in the picture of engagement check         12
17.10 Turning of pinion during engagement check                       0.5         [°]
17.11 Gear angle                                                   168.7500       [°]
17.12 Text description (Information for BOM)                      Sun
        Row 1 (BOM attribute 1)                                   Planet gear - Sun gear
        Row 2 (BOM attribute 2)                                   z0=17, mn=3, beta=20
        Row 3 (BOM attribute 3)                                   Material: 37 Cr 4
                                                                  Planet
        Row 1 (BOM attribute 1)                                   Planet gear - Planet gear
        Row 2 (BOM attribute 2)                                   z1=30, mn=3, beta=20
        Row 3 (BOM attribute 3)                                   Material: 36 Mn 5
                                                                  Ring gear
        Row 1 (BOM attribute 1)                                   Planet gear - Ring gear
        Row 2 (BOM attribute 2)                                   z2=76, mn=3, beta=20
        Row 3 (BOM attribute 3)                                   Material: 37 Cr 4


17.13 Table of parameters          Table of sun gear parameters

				
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